Products & Services
• Mobile Apps
• Services
Solutions
• Engineering, R&D
• Education
• Web & Software
• Finance, Statistics & Business Analysis
• Sciences
• Trends
Support & Learning
• Find an Answer
• Ask for Help
• Guided Learning
• Premium Support
Company
• About
• Work with Us
• Initiatives
•
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# GegenbauerC

GegenbauerC[n,m,x]
gives the Gegenbauer polynomial .

GegenbauerC[n,x]
gives the renormalized form .

## DetailsDetails

• Mathematical function, suitable for both symbolic and numerical manipulation.
• Explicit polynomials are given for integer n and for any m.
• satisfies the differential equation .
• The Gegenbauer polynomials are orthogonal on the interval with weight function , corresponding to integration over a unit hypersphere.
• For certain special arguments, GegenbauerC automatically evaluates to exact values.
• GegenbauerC can be evaluated to arbitrary numerical precision.
• GegenbauerC automatically threads over lists.
• GegenbauerC[n,0,x] is always zero.
• GegenbauerC[n,m,z] has a branch cut discontinuity in the complex z plane running from to .

## ExamplesExamplesopen allclose all

### Basic Examples  (2)Basic Examples  (2)

Compute the 10 Gegenbauer polynomial:

 Out[1]=

Compute the 10 renormalized Gegenbauer polynomial:

 Out[2]=

Plot :

 Out[1]=

## TutorialsTutorials

Introduced in 1988
(1.0)